剑指offer60 n个骰子的点数【DP】

题目描述

把n个骰子扔在地上,所有骰子朝上一面的点数之和为s。输入n,打印出s的所有可能的值出现的概率。

你需要用一个浮点数数组返回答案,其中第 i 个元素代表这 n 个骰子所能掷出的点数集合中第 i 小的那个的概率。

示例 1:

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2
输入: 1
输出: [0.16667,0.16667,0.16667,0.16667,0.16667,0.16667]

示例 2:

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2
输入: 2
输出: [0.02778,0.05556,0.08333,0.11111,0.13889,0.16667,0.13889,0.11111,0.08333,0.05556,0.02778]

限制:

1
1 <= n <= 11

解题思路

方法一:动态规划

$$
f(n,x)=\sum^{6}_{1}f(n-1,x-i)✖\frac{1}{6}
$$

代码实现

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class Solution60 {
public double[] dicesProbability(int n) {
double[] dp = new double[6];
Arrays.fill(dp, 1.0 / 6.0);
for (int i = 2; i <= n; i++) {
double[] tmp = new double[5 * i + 1];
for (int j = 0; j < dp.length; j++) {
for (int k = 0; k < 6; k++) {
tmp[j + k] += dp[j] / 6.0;
}
}
dp = tmp;
}
return dp;
}
}

复杂度分析

时间复杂度:O($n ^ 2$)

空间复杂度:O(n)

资料

Author

John Doe

Posted on

2021-06-05

Updated on

2021-06-08

Licensed under

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